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Theorem rmoeqd 2640
 Description: Equality deduction for restricted at-most-one quantifier. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
raleqd.1
Assertion
Ref Expression
rmoeqd
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rmoeqd
StepHypRef Expression
1 rmoeq1 2632 . 2
2 raleqd.1 . . 3
32rmobidv 2622 . 2
41, 3bitrd 187 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332  wrmo 2420 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rmo 2425 This theorem is referenced by: (None)
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